Macaulay2 » Documentation
Packages » ConnectionMatrices » gaugeMatrix
next | previous | forward | backward | up | index | toc

gaugeMatrix -- computes the base change over the field of rational functions

Description

Let $I = D_n\langle G\rangle$ be a $D_n$-ideal, $B$ basis of $R_n/R_nI$. This methods computes the matrix which encodes the change of basis from the set of standard monomials of $R_nI$ to the basis $B$.

i1 : D1 = makeWeylAlgebra(QQ[x, y], w1 = {2, 1});
i2 : I = ideal(x*dx^2-y*dy^2+2*dx-2*dy, x*dx+y*dy+1);

o2 : Ideal of D1
i3 : SM1 = standardMonomials I

o3 = {1, dy}

o3 : List
i4 : F = baseFractionField D1;
i5 : D2 = makeWeylAlgebra(QQ[x, y], w2 = {1, 2});
i6 : SM2 = standardMonomials sub(I, D2)

o6 = {1, dx}

o6 : List
i7 : gaugeMatrix(I, SM2)

o7 = | 1      0      |
     | (-1)/x (-y)/x |

             2      2
o7 : Matrix F  <-- F

See also

Ways to use gaugeMatrix:

  • gaugeMatrix(Ideal,List)
  • gaugeMatrix(List,List)

For the programmer

The object gaugeMatrix is a method function.


The source of this document is in /build/reproducible-path/macaulay2-1.25.06+ds/M2/Macaulay2/packages/ConnectionMatrices/docs.m2:159:0.